It could also be that Naruto has been influenced by some external force in the fanfiction. For instance, an enemy might have planted false memories or ideas in his head, making him believe that his parents and sister are bad. This false perception could then fuel his hatred.
One possible reason could be the lack of presence of his parents. Growing up without them, he might feel abandoned. And as for Konoha, if he hates it, it could be due to the way he was treated as an outcast, despite being the son of important figures. Maybe the villagers' coldness towards him made him resent the village that didn't seem to protect him from that.
One possible reason could be a misunderstanding. Maybe some false information was spread about Kushina that made Naruto believe she had wronged him in some way. And for his sister, perhaps there was some sort of jealousy or miscommunication. For example, if his sister got more attention from their father or something similar.
Perhaps they have wronged Naruto in some way in the fanfiction. They could have betrayed him, like telling his secrets to others or getting him into trouble on purpose. This would lead to Naruto developing hatred towards them.
It could be due to a misunderstanding. Perhaps there was an incident where his sister was involved, but Naruto misinterpreted her actions as something malicious against him. Like she might have accidentally broken something precious of his and he thought it was on purpose.
One possible reason could be a sense of betrayal. Maybe he discovers some long - hidden secrets about his family that make him feel they are not who he thought they were. For example, if he found out his parents had some kind of deal with the village elders that he disagreed with.
He could hate them because he felt they were absent during his difficult childhood. Naruto faced a lot of loneliness and bullying, and if he thought his parents could have prevented it but didn't, that would breed hatred.
One possible reason could be that he might feel abandoned. Growing up without them, he could resent the fact that they left him an orphan. He might think that if they were really so great, they would have found a way to survive and be there for him.
It could also be due to a prophecy. Suppose there's a prophecy that Naruto will bring great disaster in the future. His parents, believing in the prophecy, might decide to disown him in an attempt to avoid that future. They might think that by cutting ties with him, they can somehow change the course of events.
One possible reason could be some past misdeeds by the parents. Maybe they were neglectful or made decisions that seriously affected Ciel's life in a negative way in the context of the fanfic.
One possible reason could be jealousy. Maybe his brother has some special abilities or gets more attention that Naruto feels he should have. For example, if his brother is really good at a certain jutsu and is always praised for it while Naruto struggles, that could lead to resentment.